Abstract
The structure of a curved (1,0) superspace is determined by local assignments of superspace frames. The groups of superdiffeomorphisms, super-Weyl transformations and local SO(2) transformations act on the space of frames. For a general super-Riemann surface, there are frames which are not related to each other by the actions of these groups. These correspond to super-Teichmüller directions in the space of frames. A class of operators which are functionals of the (1,0) supergravity background is considered. The obstruction to factorization of their superdeterminants on parameters which describe the local structure of super-Teichmüller space is computed. This vanishes for the combination of superdeterminants associated with the supersymmetric sector of the heterotic string.
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